Is it possible to assign a hotkey on the checkbox
Yes it's possible. Go to your User Preferences, Section Input, and navigate to 3D View, Object Mode:



Then, add a hotkey for Object Mode only, and use these settings: 


Operator Name: wm.context_toggle
Hotkey: F4
Context Attribute: object.show_wire




This Operator allows you to toggle many boolean properties if they are accessible reliably via Python. You can test it by going to a Python console and typing in:

bpy.ops.wm.context_toggle(data_path='object.show_wire')


The object.show_wire part is referring to the Active Object, searching for a property called show_wire on it. so if you try this instead, the X-Ray Property will be toggled instead:

bpy.ops.wm.context_toggle(data_path='object.show_x_ray')


If you want to have the operator working for any mode in the 3D View, add the shortcut under the 3D View Global section.